A football of mass 0.450 kg is sent in the air with a speed of 16.0 m/s. It covers a distance of 30.0 m and reaches the same horizontal level as that of its initial point. If an air resistance of 0.400 N acts constantly on the football opposite to its motion during its flight, determine its final speed.
A football of mass 0.450 kg is sent in the air with a speed of 16.0 m/s. It covers a distance of 30.0 m and reaches the same horizontal level as that of its initial point. If an air resistance of 0.400 N acts constantly on the football opposite to its motion during its flight, determine its final speed.
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![**Problem:**
A football of mass 0.450 kg is sent in the air with a speed of 16.0 m/s. It covers a distance of 30.0 m and reaches the same horizontal level as that of its initial point. If an air resistance of 0.400 N acts constantly on the football opposite to its motion during its flight, determine its final speed.
**Solution:**
To determine the final speed of the football, we can use the work-energy principle. The initial kinetic energy is given by:
\[ KE_{\text{initial}} = \frac{1}{2} m v^2 = \frac{1}{2} \times 0.450 \, \text{kg} \times (16.0 \, \text{m/s})^2 \]
Calculate the initial kinetic energy.
The work done by air resistance is:
\[ W = F \times d = 0.400 \, \text{N} \times 30.0 \, \text{m} \]
Calculate the work done by air resistance.
The final kinetic energy is:
\[ KE_{\text{final}} = KE_{\text{initial}} - W \]
Finally, solve for the final speed \( v_f \):
\[ KE_{\text{final}} = \frac{1}{2} m v_f^2 \]
Substitute the values and solve for \( v_f \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fef48f1-729b-4a18-b914-3fbefd05dcf2%2Ffb774e55-1835-4761-b274-ec1825ad7277%2Fsaxbrcu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
A football of mass 0.450 kg is sent in the air with a speed of 16.0 m/s. It covers a distance of 30.0 m and reaches the same horizontal level as that of its initial point. If an air resistance of 0.400 N acts constantly on the football opposite to its motion during its flight, determine its final speed.
**Solution:**
To determine the final speed of the football, we can use the work-energy principle. The initial kinetic energy is given by:
\[ KE_{\text{initial}} = \frac{1}{2} m v^2 = \frac{1}{2} \times 0.450 \, \text{kg} \times (16.0 \, \text{m/s})^2 \]
Calculate the initial kinetic energy.
The work done by air resistance is:
\[ W = F \times d = 0.400 \, \text{N} \times 30.0 \, \text{m} \]
Calculate the work done by air resistance.
The final kinetic energy is:
\[ KE_{\text{final}} = KE_{\text{initial}} - W \]
Finally, solve for the final speed \( v_f \):
\[ KE_{\text{final}} = \frac{1}{2} m v_f^2 \]
Substitute the values and solve for \( v_f \).
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